SP- and SS-imaging for 3D elastic reverse time migration

Abstract

Three-dimensional elastic reverse time migration has been confronted with the problem of generating scalar images with vector S-waves. The underlying principle for solving this problem is to convert the vector S-waves into scalars. Previous methods were mainly focused on PS-imaging, but they usually cannot work properly on SP- and SS-cases. The complexity of SP- and SS-imaging arises from the fact that the incident S-wave has unpredictable relationship with the raypath plane. We have suggested that S-wave should be treated separately as SV- and SH-waves, which keep predictable relationships with the raypath plane. First, the elastic wavefield is separated into P- and S-waves using the Helmholtz decomposition. Then, we evaluate the normal direction of the raypath plane at each imaging grid. Next, we separate the vector S-wave obtained with curl operator into SH- and SV-waves, both of which are scalars. Finally, correlation imaging conditions are implemented to those scalar wave modes to produce scalar SV-P, SV-SV, and SH-SH images.

2D and 3D amplitude‐preserving elastic reverse time migration based on the vector‐decomposed P‐ and S‐wave records

“…Another reason is that the conventional decomposition approach produces a three‐component S‐wave, and a scalar P‐wave in the 3D case, based on which it is impossible to produce scalar reflectivity images associated with S‐wave (e.g. PS, SP, and SS images) by the conventional cross‐correlation imaging condition (Du et al ., 2014; Duan and Sava, 2015; Gong et al ., 2018). Moreover, in the 2D case, the polarity reversal problem of PS and SP images based on the conventional decomposition approach will lead to destructive migration sections (Du et al ., 2012).…”

A new scheme of wavefield decomposed elastic least-squares reverse time migration

“…The second strategy for wavefield decomposition is the decoupled wave equations (Ma and Zhu, 2003;Li et al, 2007;Zhang et al, 2007;Xiao and Leaney, 2010), which decompose wavefields by solving the P-and S-wave separated wave equations. In recent years, the decoupled wave equations prevail in elastic RTM (Wang and McMechan, 2015;Du et al, 2017;Zhou et al, 2018) and ELSRTM (Gu et al, 2018;Qu et al, 2018;Zhong et al, 2021;Shi et al, 2021;Zhang and Gao ,2022;Liu et al, 2022) because it is easy to implement and does not cause phase shift and amplitude distortion of decomposed wavefields (Duan and Sava, 2015;Du et al, 2017;Gong et al, 2018). However, if migration models are not smooth enough, the decoupled wave equation methods may suffer.…”